Thin polished plates in the form of silicon wafers are a very important part of modern technology. The requirements for flatness and thickness uniformity of these wafers are becoming more and more stringent as the printed device feature sizes are shrinking. Therefore, the metrology of these parameters is very important for development and manufacturing. Other examples for opaque polished plates are: magnetic disc substrates, gauge blocks, and the like. While the technique described here refers mainly to wafers, it is to be understood that the technique also is applicable to other types of test pieces with comparable characteristics.
Rapid and accurate simultaneous measurement of the surface height of the two sides of the wafer, and thickness variation of the wafer, is desirable for several reasons. Simultaneous measurement improves throughput, an important consideration. Another key advantage to two-sided simultaneous measurement, specifically utilizing two interferometers facing two sides of the wafer, is illustrated in FIG. 1 Wafer 100 is positioned in a cavity 103 between reference planes A(105) and B(110), which are separated by distance C(x,y) (115). At any vertical position, wafer thickness f(x,y) (120) equals distance C(x,y) minus the sum of distances dB(x,y) (125) and dA(x,y) (130) from the wafer surfaces to the reference planes.
A first method of measuring the wafer thickness uses two temporal phase shifting Fizeau inferferometers at substantially normal incidence to the wafer surface, to simultaneously obtain two single-sided distance maps between each side of a wafer and corresponding reference flats, and compute thickness variation and shape of the wafer from these data and a calibrated distance map between the two reference flats. This method is described in commonly owned U.S. Pat. No. 6,847,458, issued Jan. 25, 2005, which is hereby incorporated by reference in its entirety. In this patent, and summarized in FIG. 1, equation 140, it is shown that when measuring the wafer thickness using phase shifting interferometers to simultaneously measure the surface height on the two surfaces, the thickness measurement is independent of the flatness of the reference plates.
Accordingly, such a system is able to measure the thickness variation of a wafer without errors resulting from cavity path difference or from the shape of the reference flats. This method has been successfully used in the WaferSight measurement tool by KLA-Tencor.
The measurement principles summarized and illustrated in FIG. 1 are outlined below:
Principle of Measurements
ΦA: The calculated fringe phase of the interferogram recorded by the A side interferometer. For any point (x,y) in the phase map, it is related to the distance between the front surface of wafer and the front surface of reference flat, or dA(x,y) by
                                          d            A                    ⁡                      (                          x              ,              y                        )                          =                                            λ                              4                ⁢                π                                      ⁢                                          ϕ                A                            ⁡                              (                                  x                  ,                  y                                )                                              +                      2            ⁢            N            ⁢                                                  ⁢            π                                              (        1        )            where λ is the wavelength and N is an unknown integer. Since the unknown N is related to a constant height offset of the measurement surface, it is omitted from the interferometric measurement. Thus equation (1) becomes
                                          d            A                    ⁡                      (                          x              ,              y                        )                          =                              λ                          4              ⁢              π                                ⁢                                    ϕ              A                        ⁡                          (                              x                ,                y                            )                                                          (        2        )            Note that the equation (2) implies that the surface height computed from an interferometer carries relative height information of measuring surface only.
Similarly, ΦB is the calculated fringe phase of the interferogram recorded by the B side interferometer and
                                          d            B                    ⁡                      (                          x              ,              y                        )                          =                              λ                          4              ⁢              π                                ⁢                                    ϕ              B                        ⁡                          (                              x                ,                y                            )                                                          (        3        )            
ΦC is the calculated fringe phase of the interferogram recorded by either the A or B side interferometer and
                              C          ⁡                      (                          x              ,              y                        )                          =                              λ                          4              ⁢              π                                ⁢                                    ϕ              c                        ⁡                          (                              x                ,                y                            )                                                          (        3        )            From the figure, we can find the thicknessf=C−dA−dB  (4)This yieldsφf=φc−φA−φB  (5)Equation (5) is the key formula used in Wafersight and the present invention to calculate the phase that is related to the wafer thickness f:
                              f          ⁡                      (                          x              ,              y                        )                          =                                            λ                              4                ⁢                π                                      ⁢                                          ϕ                f                            ⁡                              (                                  x                  ,                  y                                )                                              +                      2            ⁢            N            ⁢                                                  ⁢            π                                              (        6        )            Since we do not know the integer N, we compute the wafer thickness by
                              T          ⁡                      (                          x              ,              y                        )                          =                              λ                          4              ⁢              π                                ⁢                                    ϕ              f                        ⁡                          (                              x                ,                y                            )                                                          (        7        )            Since the constant height offset of the measuring surface is omitted, the T we obtained by equation (7) is the wafer thickness variation, not the wafer thickness f.
Now let us take a look at equation (5). Before measuring the wafer, we measure a cavity map ΦC without the tilt fringe first. This is because we can only measure the cavity area that is not blocked by the wafer. This implies that the phase ΦC is measured at a time that is different from the time the ΦA and ΦB are measured. During the time difference, the spatial phase tilt may add in the cavity phase due to the reference flat move. That is why it is so important to have reference flats bigger than the wafer size so that we are able to compute the spatial phase tilt during the wafer measuring time to remove it.
A second method of measuring the surface height on both sides of a wafer, as well as its thickness variation, is described in commonly owned U.S. Pat. No. 7,009,696, issued Mar. 7, 2006, which is hereby incorporated by reference in its entirety. This method combines two grazing incidence temporal phase shifting interferometers, simultaneously obtaining front- and backside topography data, and computing thickness variation and shape of the wafer from these data. Multiple measurements of portions of the wafer are stitched together to obtain full wafer topography data maps. A flat bar in close proximity to portions of one side of the wafer provides a damping arrangement which reduces unwanted wafer vibrations during measurement. Unlike the first method, the wafer thickness variation extracted using this second method is influenced by the reference flat shape.
A refinement of the aforementioned systems and methods provides less sensitivity to vibration and air turbulence. Any method requiring multiple temporal phase-shifted frames of interferometric fringes to compute the fringe plane requires the phase-shifted frames to be taken at different times. As a result, environmental changes make phase shifts between frames deviate from what is desired. Furthermore, the second prior method has a long, non-common optical path length between the object and the reference, and is therefore more susceptible to air temperature gradients, i.e., air turbulence.
It has been recognized by the inventor, (who participated in the development of the system of U.S. Pat. No. 6,847,458, i.e. Method 1), that single shot interferometers can be utilized to perform wafer thickness measurements in the same way as the system that uses the temporal phase shifting interferometers, to preserve the insensitivity to deviations from flatness of the reference plates, and at the same time provide robustness to vibration and air turbulence. Single shot interferometers are described in one embodiment in U.S. Pat. No. 7,057,738, issued Jun. 6, 2006, which is hereby incorporated by reference in its entirety.
Single shot interferometers, including (but not limited to) spatial carrier interferometers, and simultaneous phase shifting interferometers, are able to perform accurate phase measurement of interferometric fringes by a single shot of data acquisition, in contrast to temporal phase shifting interferometers, which require multiple interferogram frames to compute the fringe phase. The single shot method thereby reduces the effects of vibration and air turbulence. Single shot interferometers have been widely used for testing large optics. They have not previously been utilized for wafer thickness measurement.
It has not been previously recognized or implemented that two such single shot interferometers can be utilized to measure wafer shape and thickness variation of two sides of a wafer simultaneously.